Related papers: Bicomplex Paley Weiner Theorem
In this paper, we study the formulae for a product of two product Euler polynomials. From this study, we derive some formulae for the integral of the product of two or more Ruler polynomials.
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
In this paper, we give some interesting identities of poly-Cauchy numbers and polynomials arising from umbral calculus.
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…
We describe the twisted doubling integrals of Cai-Friedberg-Ginzburg-Kaplan in a conceptual way. This also extends the construction to the quaternionic unitary groups. We carry out the unfolding argument uniformly in this article. To do so,…
In this paper we deal with a scale of reproducing kernel Hilbert spaces $H^{(n)}_2$, $n\ge 0$, which are linear subspaces of the classical Hilbertian Hardy space on the right-hand half-plane $\mathbb{C}^+$. They are obtained as ranges of…
Let X = G/H be a reductive symmetric space and K a maximal compact subgroup of G. The image under the Fourier transform of the space of K-finite compactly supported smooth functions on X is characterized.
We consider the $1$- and $2$-d bicomplex analogs of the classical Fourier--Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex--polyanalytic functional…
In this paper, bicomplex Pell and bicomplex Pell-Lucas numbers are defined. Also, negabicomplex Pell and negabicomplex Pell-Lucas numbers are given. Some algebraic properties of bicomplex Pell and bicomplex Pell-Lucas numbers which are…
Paley-Wiener theorem for frames for Hilbert spaces, Banach frames, Schauder frames and atomic decompositions for Banach spaces are known. In this paper, we derive Paley-Wiener theorem for p-approximate Schauder frames for separable Banach…
We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed…
In this paper, a new class of Cauchy integral formulae in superspace is obtained, using formal expansions of distributions. This allows to solve five open problems in the study of harmonic and Clifford analysis in superspace.
The aim of this paper is to extend two results from the Paley--Wiener setting to more generalmodel spaces. The first one is an analogue of the oversampling Shannon sampling formula. The second one is a version of the Donoho--Logan Large…
In this paper, we consider the poly-cauchy polynomials and numbers of the second kind which were studied by Komatsu in [10]. We note that the poly-Cauchy polynomials of the second kind are the special generalized Bernoulli polynomials of…
In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the Teichm\"uller space of analytically finite Riemann surfaces of type $(g,m)$ with $2g-2+m>0$. We also discuss a version of the F. and M.…
We consider the bilinear Fourier multiplier operator with the multiplier written as a linear combination of a fixed bump function. For those operators we prove two transference theorems, one in amalgam spaces and the other in Wiener amalgam…
A peeling theorem for the Weyl tensor in higher dimensional Lorentzian manifolds is presented. We obtain it by generalizing a proof from the four dimensional case. We derive a generic behavior, discuss interesting subcases and retrieve the…
Two novel extended semi-discrete KP-type systems, namely partial differential-difference systems with one continuous and two discrete variables, are investigated. Introducing an arbitrary function into the Cauchy matrix function or the…
This paper is concerned with the Cauchy problem for a two-component Degasperis-Procesi system. Firstly, the local well-posedness for this system in the nonhomogeneous Besov spaces is established. Then the precise blow-up scenario for strong…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…